Control an RLC Circuit Modeled as a Descriptor System

This resistor-inductor-capacitor circuit can easily be modeled from the component equations using a descriptor state-space model.

The magnitude response of the system should be reduced at the utility frequency:
Find a controller to place the closed-loop poles at symbolic locations:
Find the responses when the poles are moved away from the origin along each axis:
Moving the poles either further to the left or away from the real axis decreases the magnitude response: